Nonanalytic polarization response of a dipolar glass

The polarization response of the dipolar glass $\mathrm{K}{\mathrm{Ta}}_{1-x}{\mathrm{Nb}}_x{\mathrm{O}}_3$ ($x=0.009\mathrm{}$) over a range of temperature ($1.8 \mathrm{K}<T<\mathrm{}15\mathrm{} \mathrm{K}$) near $T_g$ is found to be a nonanalytic function of field, revealing the inadequacy of the usual nonlinear susceptibility description, as well as the incorrectness of even the linear response previously reported in such systems. A model based upon activated switching of two-level systems with a barrier distribution extending to zero energy adequately describes our data. Nonanalytic response may be a general feature of dipolar glasses, as well as other random systems, including magnetic spin glasses.